The two actors have kept their relationship quiet despite feverish speculation. Bachchan, the son of legendary Indian actor Amitabh Bachchan, first proposed to Rai in New York last week after the world premiere of "Guru," their latest film together. They made the engagement official at a small ceremony at the younger Bachchan's Mumbai residence on Sunday, an auspicious day according to the Indu calendar.

"No date for marriage has been fixed yet," says the senior Bachchan.

Rai, 33, and Bachchan, 30, have worked together on at least five films. Bachchan has about 40 films to his name.

Although not quite a U.S. household name yet, Rai has some recognition in the west. She was crowned Miss World in 1994 and starred in numerous films and music videos. She starred in the Bollywood-inspired retelling of Jane Austen's classic tale in "Bride & Prejudice" for director Gurinder Chadha ("Bend It Like Beckham") and then in "Mistress of Spices" for Paul Mayeda Berges, Chadha's husband.

She has several high-profile English-language projects in the works, including possible films opposite Brendan Fraser and Meryl Streep. She next stars opposite Colin Firth and Ben Kingsley in the epic war adventure "The Last Legion," scheduled for an April release.

A breakout English-language film role has been a long time in coming for Rai. Reports say that she's been offered numerous roles -- such as Helen in "Troy" and the lead actress in "Mr. & Mrs. Smith" -- but had to turn them down due to her packed shooting schedule.